The 27-year-old left Anfield for the Nou Camp in January 2018 for an initial fee of £105m, but he has not quite had the impact that Barcelona had hoped for.
The Brazilian has scored 21 goals in 75 appearances, but has never nailed down a guaranteed starting spot in the first XI and would suffer further if transfer targets Neymar and Antoine Griezemann arrive in Catalonia.
After winning the Copa America with Brazil this summer, Coutinho is looking to move on from his unsettled time in Spain and prefers a return to the Premier League over a switch to, interested party, Paris Saint-Germain, according to Mundo Deportivo.
However, Barca would prefer to use Coutinho as a makeweight in a deal to bring Neymar back to the club from PSG than let him return to England.
The playmaker is likely to push for his preferred option, but another problem will be that Liverpool is unwilling to pay the same amount they sold Coutinho for just 18 months ago.
The initial £105m came with the potential of add-on fees taking it to £142m, with around £13.5m of these additional fees reportedly being paid already. How high Liverpool are willing to go for their former player is yet to be seen, but it would be considerably less than the fee they received for him.
Liverpool has been quiet in the transfer market since they lifted the Champions League trophy at the start of June, only completing the signature of Sepp van den Berg from PEC Zwolle so far.
They are in the market for an addition to their front line and have been linked with the likes of Nicolas Pepe, Marcos Asensio, and Ousmane Dembele. A return for Coutinho could be the answer and his Brazil team-mate Roberto Firmino may have been greasing the wheels of a move, with the two enjoying themselves at a private party together after Brazil’s Copa America triumph over Peru.